What is (\partial)/(\partial y)(xe^{x+y}-y) ?

The answer to (\partial)/(\partial y)(xe^{x+y}-y) is xe^{x+y}-1

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(\partial)/(\partial y)(xe^{x+y}-y)

\frac{\partial}{\partial y} (x e^{x + y} - y)

x e^{x + y} - 1

Solution steps

\frac{\partial}{\partial y} (x e^{x + y} - y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (x e^{x + y}) - \frac{\partial}{\partial y} (y)

\frac{\partial}{\partial y} (x e^{x + y}) = x e^{x + y}

\frac{\partial}{\partial y} (y) = 1

= x e^{x + y} - 1

\frac{d}{d x} (4 sin (\frac{x}{2}))

\int_{- \infty}^{0} \frac{1}{7 - 9 x} d x

\frac{d}{d x} (5 e^{- 2 x} + 4)

\frac{d}{d x} (8^{4 - x^{2}})

(x^{2} - 35)^{6}

What is (\partial)/(\partial y)(xe^{x+y}-y) ?
The answer to (\partial)/(\partial y)(xe^{x+y}-y) is xe^{x+y}-1